A First Introduction to Quantum Physics - Kok, Pieter (Springer, 2018)
Quantum mechanics is one of the crowning achievements of human thought. There is no theory that is more successful in predicting phenomena over such a wide range of situations—and with such accuracy—than quantum mechanics. From the basic principles of chemistry to the working of the semiconductors in your mobile phone, and from the Big Bang to atomic clocks, quantum mechanics comes up with the goods. At the same time, we still have trouble pinpointing exactly what the theory tells us about nature. Quantum mechanics is hard, but perhaps not as hard as you think. Let us compare it to another great theory of physics: electromagnetism. When we teach electricity and magnetism in school and university, we start with simple problems involving point charges and line currents. We introduce Coulomb’s law, the law of Biot and Savart, the Lorentz force, and so on. After working through some of the most important consequences of these laws, we finally arrive at Maxwell’s equations. Advanced courses in electrodynamics then take over and explore the consequences of this unification, treating such topics as waveguides, gauge invariance, relativity. The pedagogical route is going from the simple, tangible problems to the general and abstract theory. You need to know quite a bit of electromagnetism and vector calculus before you can appreciate the beauty of Maxwell’s equations. The situation in teaching quantum mechanics is generally quite different. Instead of simple experimentally motivated problems, a first course in quantum mechanics often takes a historical approach, describing Planck’s solution of black-body radiation, Einstein’s explanation of the photoelectric effect, and Bohr’s model for the atom from 1913. This is then followed by the introduction of the Schrödinger equation. The problem is that appreciating Schrödinger’s equation requires a degree of familiarity with the corresponding classical solutions that most students do not yet have at this stage. As a result, many drown in the mathematics of solving the Schrödinger equation and never come to appreciate the subtle and counterintuitive aspects of quantum mechanics as a fundamental theory of nature.